arXiv subjects

Zhihao Bian

Publications and source records attributed to Zhihao Bian.

At least 19 recordsLinked to original sources

arXiv2026

Continuous Time Quantum Walk Propagation for Irregular Temporal Graph Forecasting

Continuous time quantum walks built on graph Laplacians produce non monotonic graph propagation features through quantum interference during evolution, which classical diffusion cannot achieve. Such walks deliver a physically motivated propagation scheme for temporal graph signal modeling. We propose Quantum Walk Temporal Architecture (QWTA), which replaces classical graph propagation with a CTQW-type parameterized spectral propagator. QWTA embeds effective observation intervals into the spectral phase modulation of the propagation kernel. QWTA-Base preserves exact CTQW spectral evolution and serves as a physically faithful propagation reference. QWTA-GR further introduces phase soft clipping and gated residual fusion to stabilize propagation. The results show that explicit phase encoding of irregular time intervals, when combined with suitable stabilization, provides a physically motivated and competitive graph propagation design for temporal graph forecasting with missing historical observations.

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arXiv2025

The detection power of real entanglement witnesses under local unitary equivalence

The imaginary unit $i$ has recently been experimentally proven to be indispensable for quantum mechanics. We study the differences in detection power between real and complex entanglement witnesses (EWs) distinguished by whether their matrix expressions incorporate imaginary parts. We show that a real EW (REW), denoted by a real Hermitian matrix, must detect one entangled state of a real density matrix, and conversely an entangled state of a real density matrix must be detected by one REW. We present a necessary and sufficient condition for the entangled states detected by REWs, and give a specific example implying the detection limitations of REWs. From an operational perspective, we investigate whether all entangled states are detected by the EWs locally equivalent to some REWs. We prove the validity for all NPT (non-positive partial transpose) states. We also derive a necessary and sufficient condition of the validity for the PPT (positive partial transpose) entangled states of complex density matrices. By this condition we show the validity for a family of two-qutrit PPT entangled states of rank four. Another way to figure out the problem is to check whether a counterexample exists. We propose a method to examine the existence from a set-theoretic perspective, and provide some supporting evidence of non-existence. Finally, we derive some results on local projections of EWs with product projectors.

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arXiv2021

Quantum information dynamics in a high-dimensional parity-time-symmetric system

Non-Hermitian systems with parity-time ($\mathcal{PT}$) symmetry give rise to exceptional points (EPs) with exceptional properties that arise due to the coalescence of eigenvectors. Such systems have been extensively explored in the classical domain, where second or higher order EPs have been proposed or realized. In contrast, quantum information studies of $\mathcal{PT}$-symmetric systems have been confined to systems with a two-dimensional Hilbert space. Here by using a single-photon interferometry setup, we simulate quantum dynamics of a four-dimensional $\mathcal{PT}$-symmetric system across a fourth-order exceptional point. By tracking the coherent, non-unitary evolution of the density matrix of the system in $\mathcal{PT}$-symmetry unbroken and broken regions, we observe the entropy dynamics for both the entire system, and the gain and loss subsystems. Our setup is scalable to the higher-dimensional $\mathcal{PT}$-symmetric systems, and our results point towards the rich dynamics and critical properties.

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arXiv2020

Conserved quantities in parity-time symmetric systems

Conserved quantities such as energy or the electric charge of a closed system, or the Runge-Lenz vector in Kepler dynamics are determined by its global, local, or accidental symmetries. They were instrumental to advances such as the prediction of neutrinos in the (inverse) beta decay process and the development of self-consistent approximate methods for isolated or thermal many-body systems. In contrast, little is known about conservation laws and their consequences in open systems. Recently, a special class of these systems, called parity-time ($\mathcal{PT}$) symmetric systems, has been intensely explored for their remarkable properties that are absent in their closed counterparts. A complete characterization and observation of conserved quantities in these systems and their consequences is still lacking. Here we present a complete set of conserved observables for a broad class of $\mathcal{PT}$-symmetric Hamiltonians and experimentally demonstrate their properties using single-photon linear optical circuit. By simulating the dynamics of a four-site system across a fourth-order exceptional point, we measure its four conserved quantities and demonstrate their consequences. Our results spell out non-local conservation laws in non-unitary dynamics and provide key elements that will underpin self-consistent analysis of non-Hermitian quantum many-body systems that are forthcoming.

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arXiv2020

Experimental demonstration of one-sided device-independent self-testing of any pure two-qubit entangled state

We demonstrate one-sided device-independent self-testing of any pure entangled two-qubit state based on a fine-grained steering inequality. The maximum violation of a fine-grained steering inequality can be used to witness certain steerable correlations, which certify all pure two-qubit entangled states. Our experimental results identify which particular pure two-qubit entangled state has been self-tested and which measurement operators are used on the untrusted side. Furthermore, we analytically derive the robustness bound of our protocol, enabling our subsequent experimental verification of robustness through state tomography. Finally, we ensure that the requisite no-signalling constraints are maintained in the experiment.

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arXiv2019

Experimental orthogonalization of highly overlapping quantum states with single photons

We experimentally realize a nonlinear quantum protocol on single-photon qubits with linear optical elements and appropriate measurements. The quantum nonlinearity is induced by post-selecting the polarization qubit based on a measurement result obtained on the spatial degree of freedom of the single photon which plays the role of a second qubit. Initially, both qubits are prepared in the same quantum state and an appropriate two-qubit unitary transformation entangles them before the measurement on the spatial part. We analyze the result by quantum state tomography on the polarization degree of freedom. We then demonstrate the usefulness of the protocol for quantum state discrimination by iteratively applying it on either one of two slightly different quantum states which rapidly converge to different orthogonal states by the iterative dynamics. Our work opens the door to employ effective quantum nonlinear evolution for quantum information processing.

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arXiv2019

Observation of critical phenomena in parity-time-symmetric quantum dynamics

We experimentally simulate non-unitary quantum dynamics using a single-photon interferometric network and study the information flow between a parity-time (PT)-symmetric non-Hermitian system and its environment. We observe oscillations of quantum-state distinguishability and complete information retrieval in the PT-symmetry-unbroken regime. We then characterize in detail critical phenomena of the information flow near the exceptional point separating the PT-unbroken and -broken regimes, and demonstrate power-law behavior in key quantities such as the distinguishability and the recurrence time. We also reveal how the critical phenomena are affected by symmetry and initial conditions. Finally, introducing an ancilla as an environment and probing quantum entanglement between the system and the environment, we confirm that the observed information retrieval is induced by a finite-dimensional entanglement partner in the environment. Our work constitutes the first experimental characterization of critical phenomena in PT-symmetric non-unitary quantum dynamics.

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arXiv2018

Higher winding number in a non-unitary photonic quantum walk

Topological matter exhibits exotic properties yet phases characterized by large topological invariants are difficult to implement, despite rapid experimental progress. A promising route toward higher topological invariants is via engineered Floquet systems, particularly in photonics, where flexible control holds the potential of extending the study of conventional topological matter to novel regimes. Here we implement a one-dimensional photonic quantum walk to explore large winding numbers. By introducing partial measurements and hence loss into the system, we detect winding numbers of three and four in multi-step non-unitary quantum walks, which agree well with theoretical predictions. Moreover, by probing statistical moments of the walker, we identify locations of topological phase transitions in the system, and reveal the breaking of pseudo-unitary near topological phase boundaries. As the winding numbers are associated with non-unitary time evolution, our investigation enriches understanding of topological phenomena in non-unitary settings.

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arXiv2018

Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics

Topology in quench dynamics gives rise to intriguing dynamic topological phenomena, which are intimately connected to the topology of static Hamiltonians yet challenging to probe experimentally. Here we experimentally detect momentum-time skyrmions in parity-time (PT)-symmetric non-unitary quench dynamics, which are protected by dynamic Chern numbers defined for the emergent momentum-time manifold. Specifically, we experimentally simulate non-unitary quench dynamics of PT-symmetric topological systems using single-photon discrete-time quantum walks, and demonstrate emergence of skyrmions by constructing the time-dependent non-Hermitian density matrix via direct measurements in position space. Our work experimentally reveals the interplay of PT symmetry and quench dynamics in inducing emergent topological structures, and highlights the application of discrete-time quantum walks for the study of dynamic topological phenomena.

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arXiv2018

Simulating dynamic quantum phase transitions in photonic quantum walks

Signaled by non-analyticities in the time evolution of physical observables, dynamic quantum phase transitions (DQPTs) emerge in quench dynamics of topological systems and possess an interesting geometric origin captured by dynamic topological order parameters (DTOPs). In this work, we report the experimental study of DQPTs using discrete-time quantum walks of single photons. We simulate quench dynamics between distinct Floquet topological phases using quantum-walk dynamics, and experimentally characterize DQPTs and the underlying DTOPs through interference-based measurements. The versatile photonic quantum-walk platform further allows us to experimentally investigate DQPTs for mixed states and in parity-time-symmetric non-unitary dynamics for the first time. Our experiment directly confirms the relation between DQPTs and DTOPs in quench dynamics of a topological system, and opens up the avenue of simulating emergent topological phenomena using discrete-time quantum-walk dynamics.

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arXiv2018

Violations of a Leggett-Garg inequality without signalling for a photonic qutrit probed with ambiguous measurements

We realise a quantum three-level system with photons distributed among three different spatial and polarization modes. Ambiguous measurement of the state of the qutrit are realised by blocking one out for the three modes at any one time. Using these measurements we construct a test of a Leggett-Garg inequality as well as tests of no-signalling-in-time for the measurements. We observe violations of the Leggett-Garg inequality that can not be accounted for in terms of signalling. Moreover, we tailor the qutrit dynamics such that both ambiguous and unambiguous measurements are simultaneously non-signalling, which is an essential step for the justification of the use of ambiguous measurements in Leggett-Garg tests.

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arXiv2018

Enhanced violations of Leggett-Garg inequalities in an experimental three-level system

Leggett-Garg inequalities are tests of macroscopic realism that can be violated by quantum mechanics. In this letter, we realise photonic Leggett-Garg tests on a three-level system and implement measurements that admit three distinct measurement outcomes, rather than the usual two. In this way we obtain violations of three- and four-time Leggett-Garg inequalities that are significantly in excess of those obtainable in standard Leggett-Garg tests. We also report violations the quantum-witness equality up to the maximum permitted for a three-outcome measurement. Our results highlight differences between spatial and temporal correlations in quantum mechanics.

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arXiv2018

Entanglement-enhanced quantum metrology in a noisy environment

Quantum metrology overcomes standard precision limits and plays a central role in science and technology. Practically it is vulnerable to imperfections such as decoherence. Here, we demonstrate quantum metrology for noisy channels such that entanglement with ancillary qubits enhances the quantum Fisher information for phase estimation but not otherwise. Our photonic experiment covers a range of noise for various types of channels, including for two randomly alternating channels such that assisted entanglement fails for each noisy channel individually. We have simulated noisy channels by implementing space-multiplexed dual interferometers with quantum photonic inputs. We have demonstrated the advantage of entanglement-assisted protocols in phase estimation experiment run with either single-probe or multi-probe approach. These results establish that entanglement with ancillae is a valuable approach for delivering quantum-enhanced metrology. Our new approach to entanglement-assisted quantum metrology via a simple linear-optical interferometric network with easy-to-prepare photonic inputs provides a path towards practical quantum metrology.

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arXiv2017

Detecting topological invariants in nonunitary discrete-time quantum walks

We report the experimental detection of bulk topological invariants in nonunitary discrete-time quantum walks with single photons. The nonunitarity of the quantum dynamics is enforced by periodically performing partial measurements on the polarization of the walker photon, which effectively introduces loss to the dynamics. The topological invariant of the nonunitary quantum walk is manifested in the quantized average displacement of the walker, which is probed by monitoring the photon loss. We confirm the topological properties of the system by observing localized edge states at the boundary of regions with different topological invariants. We further demonstrate the robustness of both the topological properties and the measurement scheme of the topological invariants against disorder.

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arXiv2017

Experimental generalized contextuality with single-photon qubits

Contextuality is a phenomenon at the heart of the quantum mechanical departure from classical behaviour, and has been recently identified as a resource in quantum computation. Experimental demonstration of contextuality is thus an important goal. The traditional form of contextuality -- as violation of a Kochen-Specker inequality -- requires a quantum system with at least three levels, and the status of the assumption of determinism used in deriving those inequalities has been controversial. By considering `unsharp' observables, Liang, Spekkens and Wiseman (LSW) derived an inequality for generalized noncontextual models that doesn't assume determinism, and applies already to a qubit. We experimentally implement the LSW test using the polarization states of a heralded single photon and three unsharp binary measurements. We violate the LSW inequality by more than 16 standard deviations, thus showing that our results cannot be reproduced by a noncontextual subset of quantum theory.

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arXiv2017

Optimal experimental demonstration of error-tolerant quantum witnesses

Testing quantum theory on macroscopic scales is a longstanding challenge that might help to revolutionise physics. For example, laboratory tests (such as those anticipated in nanomechanical or biological systems) may look to rule out macroscopic realism: the idea that the properties of macroscopic objects exist objectively and can be non-invasively measured. Such investigations are likely to suffer from i) stringent experimental requirements, ii) marginal statistical significance and iii) logical loopholes. We address all of these problems by refining two tests of macroscopic realism, or `quantum witnesses', and implementing them in a microscopic test on a photonic qubit and qutrit. The first witness heralds the invasiveness of a blind measurement; its maximum violation has been shown to grow with the dimensionality of the system under study. The second witness heralds the invasiveness of a generic quantum operation, and can achieve its maximum violation in any dimension -- it therefore allows for the highest quantum signal-to-noise ratio and most significant refutation of the classical point of view.

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arXiv2017

Centrality measure based on continuous-time quantum walks and experimental realization

Network centrality has important implications well beyond its role in physical and information transport analysis; as such, various quantum walk-based algorithms have been proposed for measuring network vertex centrality. In this work, we propose a continuous-time quantum walk algorithm for determining vertex centrality, and show that it generalizes to arbitrary graphs via a statistical analysis of randomly generated scale-free and Erdős-Rényi networks. As a proof of concept, the algorithm is detailed on a 4-vertex star graph and physically implemented via linear optics, using spatial and polarization degrees of freedoms of single photons. This paper reports the first successful physical demonstration of a quantum centrality algorithm.

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arXiv2016

Localized State in a Two-Dimensional Quantum Walk on a Disordered Lattice

We realize a pair of simultaneous ten-step one-dimensional quantum walks with two walkers sharing coins, which we prove is analogous to the ten-step two-dimensional quantum walk with a single walker holding a four-dimensional coin. Our experiment demonstrates a ten-step quantum walk over an 11x11 two-dimensional lattice with a line defect, thereby realizing a localized walker state.

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